Activation of cyclopentadienyl derivatives of transition metals with alkylalumoxanes was introduced to the art of catalysis in the mid-1970s by Kaminsky and Sinn (Angew. Chem., 88, 689 (1976)). Because these catalyst systems, when used in olefin polymerization reactors, exhibit a very strong response to hydrogen (molecular weights of polymers become greatly reduced in the presence of hydrogen), combinations of metallocene/alkylalumoxane catalyst systems with Ziegler-Natta catalyst systems provide a means of polymerizing olefins to products with broad molecular weight distributions. However, the preparation of the supported bicomponent (bimetallic) catalysts comprising metallocene/alkylalumoxane catalyst systems has a significant drawback: both the metallocene complexes and the alkylalumoxanes initially applied in the art require the use of aromatic compounds as solvents. Removal of aromatic solvents from the finished catalysts is a complex and time-consuming procedure. This invention was aimed at developing supported bimetallic catalyst systems which are synthesized in the absence of aromatic solvents and used in ethylene homopolymerization and copolymerization reactions with various alpha-olefins.